Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T08:07:39.108Z Has data issue: false hasContentIssue false
  • English
  • Français

A BIFURCATION APPROACH FOR ATTRITIONAL AND LARGE LOSSES IN CHAIN LADDER CALCULATIONS

Published online by Cambridge University Press:  13 November 2013

Ulrich Riegel
Ulrich Riegel*
Affiliation:
Swiss Re Europe S.A., Niederlassung Deutschland, 85773 Unterföhring bei München, Germany E-mail: Ulrich_Riegel@swissre.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a stochastic model for the development of attritional and large claims in long-tail lines of business and present a corresponding “chain ladder-like” IBNR method which allows the use of claims payment data for attritional and claims incurred data for large losses. We derive formulas for the mean squared error of prediction and apply the method to a German motor third party liability portfolio.

Keywords

IBNR methodchain ladderlarge lossattritional lossmean squared error of predictionstandard error
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 1 , January 2014 , pp. 127 - 172
Copyright
Copyright © ASTIN Bulletin 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Braun, Ch. (2004) The prediction error of the chain ladder method applied to correlated run-off triangles. Astin Bulletin, 34 (2), 399–423.CrossRefGoogle Scholar
[2]Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M.V. (2006) The mean square error of prediction in the chain ladder reserving method (Mack and Murphy Revisited). Astin Bulletin, 36 (2), 521–542.CrossRefGoogle Scholar
[3]Dahms, R. (2012) Linear stochastic reserving methods. Astin Bulletin, 42 (1), 1–34.Google Scholar
[4]Klugman, S.A., Panjer, H.A. and Willmot, G.E. (2004) Loss Models: From Data to Decisions, 2nd ed.New York: Wiley.Google Scholar
[5]Mack, Th. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin, 23 (2), 213–225.CrossRefGoogle Scholar
[6]Mack, Th., Quarg, G. and Braun, Ch. (2006) The mean square error of prediction in the chain ladder reserving method – A comment. Astin Bulletin, 36 (2), 543–552.CrossRefGoogle Scholar
[7]Mack, Th. (2002) Schadenversicherungsmathematik, 2nd ed.Karlsruhe:Verlag Versicherungswirtschaft.Google Scholar
[8]Quarg, G. and Mack, Th. (2004) Munich chain ladder. Blätter der DGVFM, 26 (4), 597–630.CrossRefGoogle Scholar
[9]Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Chichester: John Wiley & Sons.Google Scholar